Direct hardware solution to quadratic equation Z2⊕Z⊕β=0 in Galois fields based on normal basis representation

1988 ◽  
Vol 24 (14) ◽  
pp. 847
Author(s):  
Y.R. Shayan ◽  
Tho Le-Ngoc
Keyword(s):  
Quadratic Equation ◽  
Normal Basis ◽  
Galois Fields

scholarly journals Normal Bases on Galois Ring Extensions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng
Keyword(s):  
Signal Processing ◽  
Finite Field ◽  
Block Cipher ◽  
Field Extension ◽  
Galois Ring ◽  
Normal Basis ◽  
Galois Rings ◽  
Ring Extension ◽  
Galois Fields ◽  
Normal Bases

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.

Empirical model approach for the evaluation of pH and conductivity on pollutant diffusion in soil environment

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Mathematical Model ◽  
Quadratic Equation ◽  
Diffusivity Coefficient ◽  
Soil Environment ◽  
Irreversible Reaction ◽  
Chemical Pollutant ◽  
The Mathematical Model ◽  
Coefficient Of Diffusion ◽  
Level Of Agreement ◽  
Model Approach

This work is aimed at developing a mathematical model equation that can be used to predict the fate of contaminant in the soil environment. The mathematical model was developed based on the fundamental laws of conservation and the equation of continuity given asand was resolved to obtain a quadratic equation of the form C(X) = DX2+vX+f. The developed equation was then used to fit the experimental data that were obtained from the Physio-chemical analysis of the soil samples which were obtained at various depths; within the vicinity of the H & H Asphalt plant Company, located at Enito 3 in Ahoada West L.G.A, River State, Nigeria. The Experimental and Model results obtained from the Calculation and Simulation of the developed models were compared numerically and graphically as presented in this work. It was observed that there is reasonable level of agreement between the three results. The polynomial of the curve was established to ascertain the validity of the model; this was done for all the parameters that were analyzed. From the findings the model developed can be used to predict the concentration of a chemical pollutant at various depths. The reliability of the model developed was established giving the fact that through this quadratic equation the diffusivity (coefficient of diffusion), the water velocity and the irreversible reaction decay rate could be determined.

scholarly journals Study on Optimization of Tungsten Ore Flotation Wastewater Treatment by Response Surface Method (RSM)

Minerals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 184
Author(s):  
Liping Zhang ◽  
Xiaofei Jiao ◽  
Shengnian Wu ◽  
Xuejing Song ◽  
Ruihan Yao
Keyword(s):  
Water Glass ◽  
Suspended Solids ◽  
Good Accuracy ◽  
Ph Value ◽  
Quadratic Equation ◽  
Equation Model ◽  
Residual Water ◽  
Turbidity Removal ◽  
Design Expert ◽  
Surface Method

A large amount of collectors, inhibitors and modifiers such as oleic acid, water glass and sodium carbonate are added to the flotation processing of tungsten ore, resulting in the difficulty of the suspended solids (SS) with the residual water glass settling down in the flotation wastewater. The removal efficiency of the suspended solids is low with commonly used reagents like polyaluminium chloride (PAC) and polyacrylamide (PAM). This paper innovatively applied calcium chloride (CaCl2) to treat flotation wastewater and optimized the dosage of CaCl2, PAM and the pH value. The experimental results showed that when the dosage of 595 mg/L CaCl2 was combined with 21 mg/L PAM at pH 12, the turbidity removal ratio could reach 99.98%, and the residual turbidity of the supernatant was 0.23 NTU. The effluent could fully meet the requirements for reuse in industrial, urban miscellaneous and scenic environment water consumption (turbidity < 5 NTU). The quadratic equation model fitted with Design-Expert 8.0.6 software was constructed as Y = 91.52 + 8.68A + 1.11B − 1.02C − 1.7AB + 0.86AC + 0.06BC − 1.56A2 + 2.09B2 − 1.89C2, which had a good accuracy of the predicted responses versus the experimental data.

Sign in / Sign up

Export Citation Format

Share Document